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## Writing functions in R

Functions in R are objects that carry out operations on arguments that are supplied to them and return one or more values. The syntax for writing a function is

function (argument list) body

The first component of the function declaration is the keyword function, which indicates to R that you want to create a function. An argument list is a comma-separated list of formal arguments. A formal argument can be a symbol (i.e. a variable name such as x or y), a statement of the form symbol = expression (e.g. pch=16) or the special formal argument ... (triple dot). The body can be any valid R expression or set of R expressions. Generally, the body is a group of expressions contained in curly brackets { }, with each expression on a separate line. Functions are typically assigned to symbols, but they need not to be. This will only begin to mean anything after you have seen several examples in operation.

### Arithmetic mean of a single sample

The mean is the sum of the numbers Σy divided by the number of numbers n = Σ 1 (summing over the number of numbers in the vector called y). The R function for n is length(y) and for Σy is sum(y), so a function to compute arithmetic means is

`arithmetic.mean<-function(x)  sum(x)/length(x)`

We should test the function with some data where we know the right answer:

```y<-c(3,3,4,5,5)

arithmetic.mean(y)

[1]  4```

Needless to say, there is a built-in function for arithmetic means called mean:

```mean(y)

[1]  4```

The median ...

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